Consider a bank account which starts with dollars and pays an interest rate
per year, compounding
times per year.
- Prove that the balance in the bank account at the end of
years is
For fixed values of and
, the balance at the end of
years as
is given by
We say that money grows at the annual rate with continuous compounding if the amount of money after
years is denoted by
is given by
Give an approximate length of time for the money in a bank account to double if and compounds:
- continuously;
- four times per year.
Incomplete. Sorry, I’ll try to get back to this soon(ish).
I’ll give this a shot:
(a): There isn’t really much to prove, is there? This is just the formula for compound interest.
(b): Solve for t: 2P = Pe^(rt), ln(2) = rt, r = 0.06, so t = ln(2)/0.06.
(c): Solve for n: 2P = P*((1+0.06/4)^(4n)), 2 = ((1+0.06/4)^(4n)), log base 1.015 (2) = 4n,
(log base 1.015 (2))/4 = n.